## Group JGD_G5

Group Description ```Decomposable subspaces at degree d of the invariant ring of G5, Nicolas Thiery. Univ. Paris Sud. From Jean-Guillaume Dumas' Sparse Integer Matrix Collection, http://ljk.imag.fr/membres/Jean-Guillaume.Dumas/simc.html http://www.lapcs.univ-lyon1.fr/~nthiery/LinearAlgebra/ Linear Algebra for combinatorics Abstract: Computations in algebraic combinatorics often boils down to sparse linear algebra over some exact field. Such computations are usually done in high level computer algebra systems like MuPAD or Maple, which are reasonnably efficient when the ground field requires symbolic computations. However, when the ground field is, say Q or Z/pZ, the use of external specialized libraries becomes necessary. This document, geared toward developpers of such libraries, present a brief overview of my needs, which seems to be fairly typical in the community. IG5-6: 30 x 77 : rang = 30 (Iteratif: 0.01 s, Gauss: 0.01 s) IG5-7: 62 x 150 : rang = 62 (Iteratif: 0.02 s, Gauss: 0.01 s) IG5-8: 156 x 292 : rang = 154 (Iteratif: 0.08 s, Gauss: 0.01 s) IG5-9: 342 x 540 : rang = 308 (Iteratif: 0.46 s, Gauss: 0.02 s) IG5-10: 652 x 976 : rang = 527 (Iteratif: 2.1 s, Gauss: 0.07 s) IG5-11: 1227 x 1692 : rang = 902 (Iteratif: 7.5 s, Gauss: 0.22 s) IG5-12: 2296 x 2875 : rang = 1578 (Iteratif: 26 s, Gauss: 0.93 s) IG5-13: 3994 x 4731 : rang = 2532 (Iteratif: 80 s, Gauss: 3.35 s) IG5-14: 6727 x 7621 : rang = 3906 (Iteratif: 244 s, Gauss: 10.06 s) IG5-15: 11358 x 11987 : rang = 6146 (Iteratif: s, Gauss: 29.74 s) IG5-16: 18485 x 18829 : rang = 9519 (Iteratif: s, Gauss: 621.97 s) IG5-17: 27944 x 30131 : rang = 14060 (Iteratif: s, Gauss: 1973.8 s)```
Displaying all 13 collection matrices
Id Name Group Rows Cols Nonzeros
1977 IG5-18 JGD_G5 47,894 41,550 1,790,490
1976 IG5-17 JGD_G5 30,162 27,944 1,035,008
1975 IG5-16 JGD_G5 18,846 18,485 588,326
1974 IG5-15 JGD_G5 11,369 11,987 323,509
1973 IG5-14 JGD_G5 6,735 7,621 173,337
1972 IG5-13 JGD_G5 3,994 4,731 91,209
1971 IG5-12 JGD_G5 2,296 2,875 46,260
1970 IG5-11 JGD_G5 1,227 1,692 22,110
1969 IG5-10 JGD_G5 652 976 10,273
1968 IG5-9 JGD_G5 342 540 4,570
1967 IG5-8 JGD_G5 156 292 1,711
1966 IG5-7 JGD_G5 62 150 549
1965 IG5-6 JGD_G5 30 77 251